Consumer Theory Flashcards
What is a commodity space?
A subset of the Euclidean space (real numbers)
Define weak preference relation
If the consumer thinks bundle x is as least as good as bundle x’ , we write this as xRx’
Define strict preference relation
If xRx’ and not x’Rx , then the consumer thinks x is better than x’ . We write this as
xPx’
Define indifference relation
If xRx’ and x’Rx , then the consumer thinks x and x’ are equally good. We write this as
xIx’
What are the 3 assumptions of R
R is reflexive, i.e. xRx .
R is transitive, i.e. if xRy and yRx’ , then xRx’ .
R is connected/complete i.e. xRx’ or x’Rx
What are the 4 other possible restrictions on preferences?
Convexity
Continuity
Monotonocity
Non-satiation
Define convexity
Suppose xIx’ . Then convexity implies yPx’ and yPx
Define continuity
Suppose all bundles in A are preferred to all bundles in B. As we move from B to A, continuity implies that there exists a bundle x’ such that xIx’ .
Define monotonocity
if x > x’ , then xPx’ (i.e. more is better than less)
Define non-satiation
for every bundle x, there always exists some other bundle x’ such that x’Px
What is the slope of an indifference curve called?
marginal rate of substitution (MRS)
Define an indifference curve
A curve on a graph (the axes of which represent quantities of two commodities) linking those combinations (bundles) of quantities which the consumer regards as of equal value.
Describe the indifference curves for perfect substitutes
linear - straight lines
Describe the indifference curves for perfect complements
L shaped
Can lexicographic preferences be represented by a utility function?
No, because they are not continuous
What is MRS equal to?
(dU/dx1) / (dU/dx2)
i.e. Marginal utility wrt x1 divided by marginal utility wrt x2
What is a consumer’s budget set
The set of affordable consumption bundles
What is the slope of the budget line is equal to?
- p1/p2
What are the Marshallian demand functions for perfect complements?
x1 = x2 = m/(p1+p2)
What are the Marshallian demand functions for Cobb Douglas?
x1 = am/p1 x2 = (1-a)m/p2
What is Roy’s Identity
Given indirect utility function, Roy’s identity can be used to derive the Marshallian demand functions
x1(p1,p2,m) = - (dV/dp1) / (dV/dm) x2(p1,p2,m) = - (dV/dp2) / (dV/dm)
What is Shephard’s Lemma
Given the expenditure function, the Hicksian demand functions can be derived using Shephard’s lemma
h1(p1,p2,m) = dE/dp1 h2(p1,p2,m) = dE/dp2
How are the Indirect Utility Function and the Expenditure Function related?
The indirect utility function and the expenditure function are inverses of one another
What is the Slutsky equation?
A change in demand with respect to a change in price can be decomposed into a substitution effect and an income effect. This decomposition is given by the Slutsky equation:
dx1/dp1 = dh1/dp1 - (dx1/dm)x1
